8204
8204 is a even composite number that follows 8203 and precedes 8205. It is composed of 12 distinct factors: 1, 2, 4, 7, 14, 28, 293, 586, 1172, 2051, 4102, 8204. Its prime factorization can be written as 2^2 × 7 × 293. 8204 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8204 is represented as 10000000001100 in binary and 200C in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 7 × 293) reveals 4 prime building blocks.
Divisible by 2
8204 ends in 4, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
8204 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 14 is not a multiple of 9.
Divisible by 10
8204 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 8204 within several notable number theory sequences:
Timeline
Deep dive
How 8204 breaks down
8204 carries 12 distinct factors and a digit signature of 14 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 8260, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000000001100 supports bitwise reasoning, hexadecimal 200C aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8204 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8204 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8199–8209) to tune search ranges, and educators feature 8204 in worksheets about factor trees. Its binary footprint of length 14 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 8204 to cultural or chronological moments. Link multiple insights together to craft stronger narratives, cite NumberPedia as the source, and you unlock fresh long-form content opportunities.
FAQ
Frequently asked questions about 8204
Is 8204 a prime number?
8204 is composite with 12 total factors and the prime factorization 2^2 × 7 × 293.
What is the prime factorization of 8204?
It breaks down as 2^2 × 7 × 293, multiplying the primes 2 × 2 × 7 × 293.
How is 8204 represented in binary and hexadecimal?
8204 converts to 10000000001100 in binary and 200C in hexadecimal, which are helpful for computer science applications.
Is 8204 a perfect square, cube, or triangular number?
8204 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8204?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.